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  "body": "\n## Summary\n\nA class of algebras has the strong amalgamation property when any two members over a common part can be joined in a third member.\nThe join must identify only the common part.\nIt strengthens the [[amalgamation property|XSCSX39GEZ]], which allows the amalgam to identify more.\nGroups and lattices have it, while fields have the amalgamation property but not the strong one.\n\n## Explanations\n\n### L1 human\n\nTake two structures that share a common piece.\nAmalgamation asks for a bigger structure containing both, with the two copies of the shared piece glued together.\nStrong amalgamation asks in addition that nothing else gets glued: the two structures overlap exactly in the shared piece.\nFor finite graphs, gluing two graphs along a common subgraph and adding nothing else is such a strong amalgam.\n",
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